Trigonometry Examples

$\sqrt{\frac{1 - (- \frac{3}{5})}{1 - \frac{3}{5}}}$

Step 1

Multiply $- (- \frac{3}{5})$ .

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Step 1.1

Multiply $- 1$ by $- 1$ .

$\sqrt{\frac{1 + 1 (\frac{3}{5})}{1 - \frac{3}{5}}}$

Step 1.2

Multiply $\frac{3}{5}$ by $1$ .

$\sqrt{\frac{1 + \frac{3}{5}}{1 - \frac{3}{5}}}$

Step 2

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{5}{5} + \frac{3}{5}}{1 - \frac{3}{5}}}$

Step 3

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{5 + 3}{5}}{1 - \frac{3}{5}}}$

Step 4

Add $5$ and $3$ .

$\sqrt{\frac{\frac{8}{5}}{1 - \frac{3}{5}}}$

Step 5

Write $1$ as a fraction with a common denominator.

$\sqrt{\frac{\frac{8}{5}}{\frac{5}{5} - \frac{3}{5}}}$

Step 6

Combine the numerators over the common denominator.

$\sqrt{\frac{\frac{8}{5}}{\frac{5 - 3}{5}}}$

Step 7

Subtract $3$ from $5$ .

$\sqrt{\frac{\frac{8}{5}}{\frac{2}{5}}}$

Step 8

Multiply the numerator by the reciprocal of the denominator.

$\sqrt{\frac{8}{5} \cdot \frac{5}{2}}$

Step 9

Cancel the common factor of $2$ .

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Step 9.1

Factor $2$ out of $8$ .

$\sqrt{\frac{2 (4)}{5} \cdot \frac{5}{2}}$

Step 9.2

Cancel the common factor.

$\sqrt{\frac{2 \cdot 4}{5} \cdot \frac{5}{2}}$

Step 9.3

Rewrite the expression.

$\sqrt{\frac{4}{5} \cdot 5}$

Step 10

Cancel the common factor of $5$ .

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Step 10.1

Cancel the common factor.

$\sqrt{\frac{4}{5} \cdot 5}$

Step 10.2

Rewrite the expression.

$\sqrt{4}$

Step 11

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2}}$

Step 12

Pull terms out from under the radical, assuming positive real numbers.

$2$